Springer sthr j siegmann h magnetism from fundamentals to nanoscale dynamics (SSSsS 152 springer 2006)(ISBN 3540302824)(821s)

299 Part III Polarized Electron and X-Ray Techniques 8 Polarized Electrons and Magnetism.. In 1913 Niels Bohr 1885–1962 first postulated that the angular tum of electrons is quantized and

solid-state sciences 152

solid-state sciences

Series Editors:

M Cardona P Fulde K von Klitzing R Merlin H.-J Queisser H St¨ormerThe Springer Series in Solid-State Sciences consists of fundamental scientif ic books pre-pared by leading researchers in the f ield They strive to communicate, in a systematic andcomprehensive way, the basic principles as well as new developments in theoretical andexperimental solid-state physics

136 Nanoscale Phase Separation

and Colossal Magnetoresistance

The Physics of Manganites

and Related Compounds

in Soft Matter Physics

Micellar Solutions, Microemulsions,

Critical Phenomena

By P.K Khabibullaev and A.A Saidov

139 Optical Response of Nanostructures

Microscopic Nonlocal Theory

By K Cho

140 Fractal Concepts

in Condensed Matter Physics

By T Nakayama and K Yakubo

By Y Monarkha and K Kono

143 X-Ray Multiple-Wave Diffraction

Theory and Application

By S.-L Chang

144 Physics of Transition Metal Oxides

By S Maekawa, T Tohyama,S.E Barnes, S Ishihara,

W Koshibae, and G Khaliullin

145 Point-Contact Spectroscopy

By Y.G Naidyuk and I.K Yanson

146 Optics of Semiconductors and Their Nanostructures

Editors: H Kalt and M Hetterich

147 Electron Scattering in Solid Matter

A Theoreticaland Computational Treatise

By J Zabloudil, R Hammerling,

L Szunyogh, and P Weinberger

148 Physical Acoustics in the Solid State

By B L¨uthi

149 Solitary Waves

in Complex Dispersive Media

Theory· Simulation · Applications

By V.Yu Belashov andS.V Vladimirov

150 Topology in Condensed Matter

Editor: M.I Monastyrsky

151 Particle Penetration and Radiation Effects

By P Sigmund

152 Magnetism

From Fundamentals

to Nanoscale Dynamics

By J St¨ohr and H.C Siegmann

Volumes 90–135 are listed at the end of the book

Professor Dr Hans Christoph Siegmann

Stanford Synchrotron Radiation Laboratory

P.O Box 20450, Mail Stop 69, Stanford, CA 94309, USA

E-mail: Stohr@slac.stanford.edu, Siegmann@slac.stanford.edu

Series Editors:

Professor Dr., Dres h c Manuel Cardona

Professor Dr., Dres h c Peter Fulde∗

Professor Dr., Dres h c Klaus von Klitzing

Professor Dr., Dres h c Hans-Joachim Queisser

Max-Planck-Institut f¨ur Festk¨orperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany

∗Max-Planck-Institut f¨ur Physik komplexer Systeme, N¨othnitzer Strasse 38

01187 Dresden, Germany

Professor Dr Roberto Merlin

Department of Physics, 5000 East University, University of Michigan

Ann Arbor, MI 48109-1120, USA

Professor Dr Horst St¨ormer

Dept Phys and Dept Appl Physics, Columbia University, New York, NY 10027 and

Bell Labs., Lucent Technologies, Murray Hill, NJ 07974, USA

ISSN 0171-1873

ISBN-10 3-540-30282-4 Springer Berlin Heidelberg New York

ISBN-13 978-3-540-30282-7 Springer Berlin Heidelberg New York

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my mother Marga, my wife Linda and my daughter Megan,

who have taught me much more than science and given me the most important gift of all, love.

J St¨ ohr

To my collaborators and students who, through their inspiration and company, have made my life as a physicist a joyful adventure.

H.C Siegmann

This book emerged from a close collaboration of the authors which started inthe fall of 2000 Early that year one of us (J.S.) had joined the Stanford facultyafter spending nearly 15 years at the IBM Almaden Research Center and theother (H.C.S.) had just retired from a chair at the ETH Z¨urich and come toStanford as a visiting professor Together we organized magnetism meetings

of a small group of scientists which oscillated weekly between the StanfordSynchrotron Radiation Laboratory (SSRL) and the Advanced Light Source(ALS) in nearby Berkeley We also organized annual winter workshops at LakeTahoe where all participants reported on their research – of course we snuck

in a few ski runs, as well These meetings were great fun and some seemed

to go on forever because there was so much interest and enthusiasm and somuch to discuss The participants varied over the years and consisted of stu-dents, postdocs, Stanford and Berkeley scientists, visiting scientists and par-ticipants from industry In alphabetical order, some of the people involved wereYves Acremann, Scott Andrews, Andreas Bauer, Mark Burkhardt, VenkateshChembrolu, Kang Chen, Sug-Bong Choe, Bruce Clemens, Alexander Dobin,Thomas Eim¨uller, Stefan Eisebitt, Sara Gamble, Alexander Kashuba, MarcusL¨orgen, Jan L¨uning, Gereon Meyer, Hendrik Ohldag, Howard Padmore, Ra-mon Rick, Andreas Scherz, Bill Schlotter, Andreas Scholl, Christian Stamm,John Paul Strachan, Jan Thiele, Ioan Tudosa, Ashwin Tulapurkar, Shan Wangand Xiaowei Yu All this would have been impossible without support fromthe Office of Basic Energy Sciences of the US Department of Energy (DOE),and we gratefully acknowledge DOE’s support of our research program

We have also greatly benefitted from discussions with colleagues and frommaterial they have provided, and we would especially like to thank Elke Aren-holz, Sam Bader, Carl Bennemann, Matthias Bode, Patrick Bruno, John Clen-denin, Markus Donath, Olle Eriksson, J¨urgen Kirschner, Peter Oppeneer, J¨urgOsterwalder, Stuart Parkin, Danilo Pescia, Dan Pierce, Theo Rasing, AndreiRogalev, Kai Starke, Dieter Weller and Ruqian Wu

With the present book we intend to give an account of the historical velopment, the physical foundations and the continuing research underlying

de-the field of magnetism, one of de-the oldest and still vital field of physics Ourbook is written as a text book for students on the late undergraduate andthe graduate levels It should also be of interest to scientists in academia andresearch laboratories.

Throughout history, magnetism has played an important role in the velopment of civilization, starting with the loadstone compass Our modernsociety would be unthinkable without the generation and utilization of elec-tricity, wireless communication at the speed of light and the modern high-tech magnetic devices used in information technology Despite the existence

de-of many books on the topic, we felt the need for a text book that reviews thefundamental physical concepts and uses them in a coherent fashion to explainsome of the forefront problems and applications today Besides covering theclassical concepts of magnetism we give a thorough review of the quantumaspects of magnetism, starting with the discovery of the spin in the 1920s

We discuss the exciting developments in magnetism research and technologyspawned by the computer revolution in the late 1950s and the more recentparadigm shift starting around 1990 associated with spin-based electronics or

“spintronics” The field of spintronics was largely triggered by the discovery

of the giant magnetoresistance or GMR effect around 1988 It utilizes theelectron spin to sense, carry or manipulate information and has thus movedthe quantum mechanical concept of the electron spin from its discovery in the1920s to a cornerstone of modern technology

These historical and modern developments in magnetism are discussedagainst the background of the development and utilization of spin-polarizedelectron techniques and polarized photon techniques, the specialties of theauthors It is believed that the technological application of magnetism willcontinue with a growth rate close to Moore’s law for years to come Interest-ingly, the magnetic technology goals of “smaller and faster” are matched by

“brighter and faster” X-ray sources, which are increasingly used in rary magnetism research Novel ultra-bright X-ray sources with femtosecondpulse lengths will provide us with snapshots of the invisible ultrafast magneticnanoworld These exciting developments are another reason for the presentbook

contempo-Last not least, this book is born out of our passion for the subjects cussed in it In the process we had to get to the bottom of many things andunderstand them better or for the first time This process took a deep com-mitment and much time, with “the book” often preoccupying our minds Theprocess was greatly aided by discussions with our colleagues and students and

dis-we would like to thank them at this place In particular, dis-we need to thankIoan Tudosa for his critical comments and for helping us with numerous il-lustrations In this book we give an account of the field of magnetism that iscolored by personal taste and our way of looking at things We hope that youwill enjoy the result

1 Introduction 1

1.1 Magnetism: Magical yet Practical 1

1.2 History of Magnetism 3

1.3 Magnetism, Neutrons, Polarized Electrons, and X-rays 12

1.3.1 Spin Polarized Electrons and Magnetism 15

1.3.2 Polarized X-rays and Magnetism 22

1.4 Developments in the Second Half of the 20th Century 25

1.5 Some Thoughts about the Future 30

1.6 About the Present Book 32

Part I Fields and Moments 2 Electric Fields, Currents, and Magnetic Fields 39

2.1 Signs and Units in Magnetism 39

2.2 The Electric Field 39

2.3 The Electric Current and its Magnetic Field 40

2.4 High Current Densities 45

2.5 Magnetic and Electric Fields inside Materials 47

2.6 The Relation of the Three Magnetic Vectors in Magnetic Materials 49

2.6.1 Stray and Demagnetizing Fields of Thin Films 52

2.6.2 Applications of Stray and Demagnetizing Fields 54

2.7 Symmetry Properties of Electric and Magnetic Fields 57

2.7.1 Parity 57

2.7.2 Time Reversal 59

3 Magnetic Moments and their Interactions with Magnetic Fields 61

3.1 The Classical Definition of the Magnetic Moment 61

3.2 From Classical to Quantum Mechanical Magnetic Moments 64

3.2.1 The Bohr Magneton 65

3.2.2 Spin and Orbital Magnetic Moments 66

3.3 Magnetic Dipole Moments in an External Magnetic Field 68

3.4 The Energy of a Magnetic Dipole in a Magnetic Field 69

3.5 The Force on a Magnetic Dipole in an Inhomogeneous Field 72

3.5.1 The Stern–Gerlach Experiment 74

3.5.2 The Mott Detector 79

3.5.3 Magnetic Force Microscopy 83

3.6 The Torque on a Magnetic Moment in a Magnetic Field 84

3.6.1 Precession of Moments 85

3.6.2 Damping of the Precession 87

3.6.3 Magnetic Resonance 91

3.7 Time–Energy Correlation 97

3.7.1 The Heisenberg Uncertainty Principle 97

3.7.2 Classical Spin Precession 98

3.7.3 Quantum Mechanical Spin Precession 99

4 Time Dependent Fields 105

4.1 Overview 105

4.2 Basic Concepts of Relativistic Motion 106

4.2.1 Length and Time Transformations Between Inertial Systems 106

4.2.2 Electric and Magnetic Field Transformations between Inertial Systems 107

4.3 Fields of a Charge in Uniform Motion: Velocity Fields 109

4.3.1 Characteristics of Velocity Fields 109

4.3.2 Creation of Large Currents and Magnetic Fields 112

4.3.3 Creation of Ultrashort Electron Pulses and Fields 115

4.3.4 The Temporal Nature of Velocity Fields 118

4.4 Acceleration Fields: Creation of EM Radiation 121

4.4.1 Polarized X-rays: Synchrotron Radiation 125

4.4.2 Brighter and Shorter X-ray Pulses: From Undulators to Free Electron Lasers 133

5 Polarized Electromagnetic Waves 141

5.1 Maxwell’s Equations and their Symmetries 142

5.2 The Electromagnetic Wave Equation 143

5.3 Intensity, Flux, Energy, and Momentum of EM Waves 145

5.4 The Basis States of Polarized EM Waves 147

5.4.1 Photon Angular Momentum 147

5.4.2 Linearly Polarized Basis States 148

5.4.3 Circularly Polarized Basis States 149

5.4.4 Chirality and Angular Momentum of Circular EM Waves 153

5.4.5 Summary of Unit Polarization Vectors 154

5.5 Natural and Elliptical Polarization 155

5.5.1 Natural Polarization 155

5.5.2 Elliptical Polarization 156

5.5.3 The Degree of Photon Polarization 157

5.6 Transmission of EM Waves through Chiral and Magnetic Media 159

Part II History and Concepts of Magnetic Interactions 6 Exchange, Spin–Orbit, and Zeeman Interactions 167

6.1 Overview 167

6.2 The Spin Dependent Atomic Hamiltonian or Pauli Equation 169

6.2.1 Independent Electrons in a Central Field 170

6.2.2 Interactions between two Particles – Symmetrization Postulate and Exclusion Principle 172

6.3 The Exchange Interaction 175

6.3.1 Electron Exchange in Atoms 175

6.3.2 Electron Exchange in Molecules 180

6.3.3 Magnetism and the Chemical Bond 186

6.3.4 From Molecules to Solids 188

6.3.5 The Heisenberg Hamiltonian 190

6.3.6 The Hubbard Hamiltonian 193

6.3.7 Heisenberg and Hubbard Models for H2 195

6.3.8 Summary and Some General Rules for Electron Exchange 202

6.4 The Spin–Orbit Interaction 203

6.4.1 Fine Structure in Atomic Spectra 203

6.4.2 Semiclassical Model for the Spin–Orbit Interaction 204

6.4.3 The Spin–Orbit Hamiltonian 206

6.4.4 Importance of the Spin–Orbit Interaction 209

6.5 Hund’s Rules 209

6.6 The Zeeman Interaction 212

6.6.1 History and Theory of the Zeeman Effect 212

6.6.2 Zeeman Versus Exchange Splitting of Electronic States 218 6.6.3 Importance of the Zeeman Interaction 220

7 Electronic and Magnetic Interactions in Solids 221

7.1 Chapter Overview 221

7.2 Localized versus Itinerant Magnetism: The Role of the Centrifugal Potential 223

7.3 The Relative Size of Interactions in Solids 230

7.4 The Band Model of Ferromagnetism 234

7.4.1 The Puzzle of the Broken Bohr Magneton Numbers 234

7.4.2 The Stoner Model 235

7.4.3 Origin of Band Structure 240

7.4.4 Density Functional Theory 243

7.5 Ligand Field Theory 245

7.5.1 Independent-Electron Ligand Field Theory 247

7.5.2 Multiplet Ligand Field Theory 256

7.6 The Importance of Electron Correlation and Excited States 261

7.6.1 Why are Oxides often Insulators? 262

7.6.2 Correlation Effects in Rare Earths and Transition Metal Oxides 264

7.6.3 From Delocalized to Localized Behavior: Hubbard and LDA+U Models 271

7.7 Magnetism in Transition Metal Oxides 274

7.7.1 Superexchange 274

7.7.2 Double Exchange 279

7.7.3 Colossal Magnetoresistance 282

7.7.4 Magnetism of Magnetite 283

7.8 RKKY Exchange 290

7.8.1 Point-like Spins in a Conduction Electron Sea 291

7.8.2 Metallic Multilayers 292

7.9 Spin–Orbit Interaction: Origin of the Magnetocrystalline Anisotropy 294

7.9.1 The Bruno Model 295

7.9.2 Description of Anisotropic Bonding 297

7.9.3 Bonding, Orbital Moment, and Magnetocrystalline Anisotropy 299

Part III Polarized Electron and X-Ray Techniques 8 Polarized Electrons and Magnetism 313

8.1 Introduction 313

8.2 Generation of Spin-Polarized Electron Beams 314

8.2.1 Separation of the Two Spin States 314

8.2.2 The GaAs Spin-Polarized Electron Source 315

8.3 Spin-Polarized Electrons and Magnetic Materials: Overview of Experiments 318

8.4 Formal Description of Spin-Polarized Electrons 319

8.4.1 Quantum Behavior of the Spin 319

8.4.2 Single Electron Polarization in the Pauli Spinor Formalism 320

8.4.3 Description of a Spin-Polarized Electron Beam 324

8.5 Description of Spin Analyzers and Filters 327

8.5.1 Incident Beam Polarization: Spin Analyzer 327

8.5.2 Transmitted Beam Polarization: Spin Filter 328

8.5.3 Determination of Analyzer Parameters 329

8.6 Interactions of Polarized Electrons with Materials 329

8.6.1 Beam Transmission through a Spin Filter 329

8.6.2 The Fundamental Interactions of a Spin-Polarized Beam with Matter 331

8.6.3 Interaction of Polarized Electrons with Magnetic Materials: Poincar´e’s Sphere 337

8.7 Link Between Electron Polarization and Photon Polarization 342 8.7.1 Photon Polarization in the Vector Field Representation343 8.7.2 Photon Polarization in the Spinor Representation 344

8.7.3 Transmission of Polarized Photons through Magnetic Materials: Poincar´e Formalism 345

8.7.4 X-ray Faraday Effect and Poincar´e Formalism 348

8.7.5 Poincar´e and Stokes Formalism 350

9 Interactions of Polarized Photons with Matter 351

9.1 Overview 351

9.2 Terminology of Polarization Dependent Effects 352

9.3 SemiClassical Treatment of X-ray Scattering by Charges and Spins 355

9.3.1 Scattering by a Single Electron 355

9.3.2 Scattering by an Atom 360

9.4 SemiClassical Treatment of Resonant Interactions 361

9.4.1 X-ray Absorption 361

9.4.2 Resonant Scattering 364

9.4.3 Correspondence between Resonant Scattering and Absorption 368

9.4.4 The Kramers–Kronig Relations 368

9.5 Quantum-Theoretical Concepts 370

9.5.1 One-Electron and Configuration Pictures of X-ray Absorption 370

9.5.2 Fermi’s Golden Rule and Kramers–Heisenberg Relation372 9.5.3 Resonant Processes in the Electric Dipole Approximation 374

9.5.4 The Polarization Dependent Dipole Operator 376

9.5.5 The Atomic Transition Matrix Element 378

9.5.6 Transition Matrix Element for Atoms in Solids 381

9.6 The Orientation-Averaged Intensity: Charge and Magnetic Moment Sum Rules 385

9.6.1 The Orientation-Averaged Resonance Intensity 385

9.6.2 Derivation of the Intensity Sum Rule for the Charge 386

9.6.3 Origin of the XMCD Effect 389

9.6.4 Two-Step Model for the XMCD Intensity 393

9.6.5 The Orientation Averaged Sum Rules 397

9.7 The Orientation-Dependent Intensity: Charge and Magnetic

Moment Anisotropies 401

9.7.1 Concepts of Linear Dichroism 401

9.7.2 X-ray Natural Linear Dichroism 401

9.7.3 Theory of X-ray Natural Linear Dichroism 403

9.7.4 XNLD and Quadrupole Moment of the Charge 406

9.7.5 X-ray Magnetic Linear Dichroism 407

9.7.6 Simple Theory of X-ray Magnetic Linear Dichroism 408

9.7.7 XMLD of the First and Second Kind 411

9.7.8 Enhanced XMLD through Multiplet Effects 415

9.7.9 The Orientation-Dependent Sum Rules 421

9.8 Magnetic Dichroism in X-ray Absorption and Scattering 424

9.8.1 The Resonant Magnetic Scattering Intensity 425

9.8.2 Link of Magnetic Resonant Scattering and Absorption 427 10 X-rays and Magnetism: Spectroscopy and Microscopy 431

10.1 Introduction 431

10.2 Overview of Different Types of X-ray Dichroism 432

10.3 Experimental Concepts of X-ray Absorption Spectroscopy 437

10.3.1 General Concepts 437

10.3.2 Experimental Arrangements 441

10.3.3 Quantitative Analysis of Experimental Absorption Spectra 445

10.3.4 Some Important Experimental Absorption Spectra 449

10.3.5 XMCD Spectra of Magnetic Atoms: From Thin Films to Isolated Atoms 451

10.3.6 Sum Rule Analysis of XMCD Spectra: Enhanced Orbital Moments in Small Clusters 454

10.3.7 Measurement of Small Spin and Orbital Moments: Pauli Paramagnetism 457

10.4 Magnetic Imaging with X-rays 458

10.4.1 X-ray Microscopy Methods 459

10.4.2 Lensless Imaging by Coherent Scattering 463

10.4.3 Overview of Magnetic Imaging Results 468

Part IV Properties of and Phenomena in the Ferromagnetic Metals 11 The Spontaneous Magnetization, Anisotropy, Domains 479

11.1 The Spontaneous Magnetization 480

11.1.1 Temperature Dependence of the Magnetization in the Molecular Field Approximation 481

11.1.2 Curie Temperature in the Weiss–Heisenberg Model 484

11.1.3 Curie Temperature in the Stoner Model 488

11.1.4 The Meaning of “Exchange” in the Weiss–Heisenberg

and Stoner Models 491

11.1.5 Thermal Excitations: Spin Waves 494

11.1.6 Critical Fluctuations 499

11.2 The Magnetic Anisotropy 504

11.2.1 The Shape Anisotropy 507

11.2.2 The Magneto-Crystalline Anisotropy 508

11.2.3 The Discovery of the Surface Induced Magnetic Anisotropy 510

11.3 The Magnetic Microstructure: Magnetic Domains and Domain Walls 511

11.3.1 Ferromagnetic Domains 511

11.3.2 Antiferromagnetic Domains 515

11.4 Magnetization Curves and Hysteresis Loops 515

11.5 Magnetism in Small Particles 517

11.5.1 N´eel and Stoner–Wohlfarth Models 517

11.5.2 Thermal Stability 520

12 Magnetism of Metals 521

12.1 Overview 521

12.2 Band Theoretical Results for the Transition Metals 523

12.2.1 Basic Results for the Density of States 523

12.2.2 Prediction of Magnetic Properties 525

12.3 The Rare Earth Metals: Band Theory versus Atomic Behavior 530 12.4 Spectroscopic Tests of the Band Model of Ferromagnetism 534

12.4.1 Spin Resolved Inverse Photoemission 535

12.4.2 Spin Resolved Photoemission 539

12.5 Resistivity of Transition Metals 548

12.5.1 Conduction in Nonmagnetic Metals 548

12.5.2 The Two Current Model 553

12.5.3 Anisotropic Magnetoresistance of Metals 556

12.6 Spin Conserving Electron Transitions in Metals 558

12.6.1 Spin Conserving Transitions and the Photoemission Mean Free Path 558

12.6.2 Determination of the Spin-Dependent Mean Free Path using the Magnetic Tunnel Transistor 562

12.6.3 Probability of Spin-Conserving relative to Spin-Non-Conserving Transitions 565

12.6.4 The Complete Spin-Polarized Transmission Experiment569 12.7 Transitions Between Opposite Spin States in Metals 573

12.7.1 Classification of Transitions Between Opposite Spin States 573

12.7.2 The Detection of Transitions between Opposite Spin States 575

12.8 Remaining Challenges 582

Part V Topics in Contemporary Magnetism

13 Surfaces and Interfaces of Ferromagnetic Metals 587

13.1 Overview 587

13.2 Spin-Polarized Electron Emission from Ferromagnetic Metals 588 13.2.1 Electron Emission into Vacuum 588

13.2.2 Spin-Polarized Electron Tunneling between Solids 593

13.2.3 Spin-Polarized Electron Tunneling Microscopy 598

13.3 Reflection of Electrons from a Ferromagnetic Surface 601

13.3.1 Simple Reflection Experiments 603

13.3.2 The Complete Reflection Experiment 608

13.4 Static Magnetic Coupling at Interfaces 613

13.4.1 Magnetostatic Coupling 614

13.4.2 Direct Coupling between Magnetic Layers 615

13.4.3 Exchange Bias 617

13.4.4 Induced Magnetism in Paramagnets and Diamagnets 629

13.4.5 Coupling of Two Ferromagnets across a Nonmagnetic Spacer Layer 632

14 Electron and Spin Transport 637

14.1 Currents Across Interfaces Between a Ferromagnet and a Nonmagnet 637

14.1.1 The Spin Accumulation Voltage in a Transparent Metallic Contact 638

14.1.2 The Diffusion Equation for the Spins 642

14.1.3 Spin Equilibration Processes, Distances and Times 644

14.1.4 Giant Magneto-Resistance (GMR) 647

14.1.5 Measurement of Spin Diffusion Lengths in Nonmagnets 651 14.1.6 Typical Values for the Spin Accumulation Voltage, Boundary Resistance and GMR Effect 654

14.1.7 The Important Role of Interfaces in GMR 655

14.2 Spin-Injection into a Ferromagnet 656

14.2.1 Origin and Properties of Spin Injection Torques 657

14.2.2 Switching of the Magnetization with Spin Currents: Concepts 665

14.2.3 Excitation and Switching of the Magnetization with Spin Currents: Experiments 667

14.3 Spin Currents in Metals and Semiconductors 672

14.4 Spin-Based Transistors and Amplifiers 675

15 Ultrafast Magnetization Dynamics 679

15.1 Introduction 679

15.2 Energy and Angular Momentum Exchange between Physical Reservoirs 682

15.2.1 Thermodynamic Considerations 682

15.2.2 Quantum Mechanical Considerations: The Importance of Orbital Angular Momentum 684

15.3 Spin Relaxation and the Pauli Susceptibility 687

15.4 Probing the Magnetization after Laser Excitation 690

15.4.1 Probing with Spin-Polarized Photoelectron Yield 691

15.4.2 Probing with Energy Resolved Photoelectrons With or Without Spin Analysis 696

15.4.3 Probing with the Magneto-Optic Kerr Effect 702

15.5 Dynamics Following Excitation with Magnetic Field Pulses 705

15.5.1 Excitation with Weak Magnetic Field Pulses 712

15.5.2 Excitation of a Magnetic Vortex 715

15.6 Switching of the Magnetization 723

15.6.1 Precessional Switching of the In-Plane Magnetization 725 15.6.2 Precessional Switching of the Magnetization for Perpendicular Recording Media 733

15.6.3 Switching by Spin Injection and its Dynamics 744

15.6.4 On the Possibility of All-Optical Switching 751

15.6.5 The H¨ubner Model of All-Optical Switching 753

15.6.6 All-Optical Manipulation of the Magnetization 757

15.7 Dynamics of Antiferromagnetic Spins 759

Part VI Appendices Appendices 763

A.1 The International System of Units (SI) 763

A.2 The Cross Product 765

A.3 s, p, and d Orbitals 766

A.4 Spherical Tensors 767

A.5 Sum Rules for Spherical Tensor Matrix Elements 768

A.6 Polarization Dependent Dipole Operators 769

A.7 Spin–Orbit Basis Functions for p and d Orbitals 770

A.8 Quadrupole Moment and the X-ray Absorption Intensity 771

A.9 Lorentzian Line Shape and Integral 774

A.10 Gaussian Line Shape and Its Fourier Transform 774

A.11 Gaussian Pulses, Half-Cycle Pulses and Transforms 775

References 777

Index 805

Magnetes Geheimnis, erkl¨ ar mir das! Kein gr¨ oßer Geheimnis als Lieb’ und Hass The magnet’s mystery, explain that to me!

No greater mystery but love and hate.1

Johann Wolfgang von Goethe (1749–1832)

1.1 Magnetism: Magical yet Practical

What is magnetism? This question has fascinated people ever since Thales ofMiletus (about 634–546 BC) first described the phenomenon as the attrac-tion of iron by “lodestone”, the naturally occurring mineral magnetite, Fe3O4.Over the last 2,500 years we have not only extensively used the phenomenonfor navigation, power production, and “high tech” applications but we havealso come a long way in exploring its origin Yet, even today, it is extremelydifficult to answer the simple question why magnets attract In fact, the term

“magnetic” has acquired such a fundamental and familiar meaning that, lowing Thales of Miletus, “magnetic” and “attractive” (or repulsive) are usedsynonymously, and this association still serves to “explain” the phenomenon.Any deeper scientific explanation sooner or later runs into “mysteries” Anexample is the very concept of spin which magically emerged from Dirac’s rela-tivistic treatment of an electron in an external electromagnetic field Today

fol-we simply accept this concept and base our understanding of magnetism onthe elementary concepts of spin, giving rise to the spin magnetic moment, andthe motion of electronic charges and the associated orbital magnetic moment

Of the four forces of nature that form the pillars of contemporary physics,the electromagnetic force is arguably of greatest importance in our everydaylives because we can easily manipulate it and hence utilize it for our needs

We truly live in an electromagnetic world and electromagnetic phenomenaform the basis of the modern industrialized society This fact alone gives theold topic of magnetism a modern day vitality The importance of magnetism1

For Goethe the magnet constitutes a fundamental phenomenon (Urph¨anomen)that cannot be further explained It incorporates the polarity (like love and hate)which became the essence of Goethe’s “Weltanschauung” In this “natural philo-sophy” only pairwise opposites (e.g., love–hate, north–south) constitute a “whole” It

is interesting that this philosophy agrees with our modern knowledge of magnetism,i.e., that no magnetic monopoles have been found

is enhanced by the fact that the field still undergoes dynamic developments.Ever new magnetic phenomena continue to be discovered in conjunction withour ability to atomically engineer new materials.

As throughout history, today’s magnetism research remains closely tied

to applications It is therefore no surprise that some of the forefront researchareas in magnetism today are driven by the “smaller and faster” mantra of ad-vanced technology The goal to develop, understand, and control the ultrafastmagnetic nanoworld is furthermore accompanied by the development of newexperimental techniques, that offer capabilities not afforded by conventionaltechniques We shall see below that polarized electrons and X-rays provide uswith unprecedented opportunities to get to the bottom of long standing andnovel problems At the brink of the 21st century we find ourselves in a situ-ation where the old field of magnetism is full of vitality, life, and excitementand this fact constitutes the basis for our book

Because magnetism is one of the oldest scientific topics there is of course(too) much to write about It is therefore not easy to find the right emphasis

on the many concepts, definitions, laws and the experimental and theoreticaldevelopments of this old and broad field Our book aims at discussing funda-mental concepts and modern applications of magnetism and we have selectedtopics based on three main principles First, they were chosen to be the fun-damental pillars of magnetism Second, we emphasized those fundamentalswith applications in modern magnetism research and technology Third, weemphasized topics where new experimental approaches such as polarized elec-tron beam and X-ray experiments, the specialties of the authors, have led tonew insights and promise further breakthroughs in the future In many cases

we have chosen modern applications to illustrate the basic laws

Rather than covering all aspects of magnetism, our book concentrates onmagnetic phenomena that are the subject of modern conferences on mag-netism and magnetic materials Today’s magnetism community is interested

in the scientific understanding of magnetic phenomena and magnetic rials and, following the historical trend, is clearly motivated and influenced

mate-by the goal to utilize the acquired knowledge for technological advancement.Our treatment therefore does not cover other electron correlation phenomenawhich give rise to interesting charge and spin ordering effects, and may play

an important role in high temperature superconductivity, for example Thesephenomena deserve an extensive separate treatment since they are causing aparadigm shift in condensed matter physics

It is only fitting that we start this book by taking a look at the historicaldevelopment of the field Some of the magnetism terminology used in thisintroduction is not explicitly defined but we shall come back to the importantaspects later in this book The following historical review is based on informa-tion from many sources We found the books by Segr`e [1,2], Verschuur [3] andLivingston [4] very valuable In the age of the internet, much information wasgathered and checked for consistency by means of searches and comparisons

of sources on the world wide web

1.2 History of Magnetism

The most primitive electrical and magnetic phenomena were no doubt erved before recorded history began, and they are perhaps the oldest topics

obs-in physics Accordobs-ing to Plobs-iny the Elder’s (23–79 AD) Historia Naturalis

the name “magnet” came from a shepherd called Magnes, who found his nailed shoes or iron-tipped cane stuck to the ground.2It seems more likely thatthe name originates from Magnetes, the inhabitants of a town called Magnesia,located in Asia Minor (part of the Greek Empire), who knew about ore in thearea nearby that was naturally magnetic Since around 1500 AD, the name

iron-lodestone (“lode” being old English for “lead”) has been used to describe

such magnetic ore because of its use in navigation Today we more specificallyassociate lodestone with the spinel magnetite, Fe3O4, which is magneticallyaligned in nature, most likely by the earth’s magnetic field during the coolingprocess of hot lava

Local alignment may also occur by the strong magnetic field of a lightningbolt that leaves a characteristic circular pattern around the point of impact asshown in Fig 1.1 [5–8] A lightning bolt contains a current of the order of 100

A

CDB

Current

Ground

Towerpost

iron-around the four feet of the transmission-line tower labelled A, B, C, and D [5] Themagnetization (arrows) in the iron-oxide rock is seen to follow the circular magneticfield around the four points

2The smelting of iron was developed already around 1200 BC

Fig 1.2 Working model of the first instrument known to be a compass, called Si

Nan (the south governor) by the Chinese The spoon is of magnetic lodestone, andthe plate is of bronze [10]

kA with a typical current density of 105A/m2in a flash of a few microsecondsduration The current direction (flow of positive charge) is typically from theground to the clouds, i.e., is in the opposite direction as that observed in thecase shown in Fig 1.1

The first definite statement on magnetism is attributed to Thales of tus (about 634–546 BC) who said that lodestone attracts iron Starting withthe Chinese writer Guanzhong (died 645 BC) the Chinese literature in later

Mile-centuries is also full of references to lodestone, called ci shi, the “loving stone”

because of its ability to attract iron [9] It is believed that the first directionpointers were made during the Qin dynasty (221–206 BC) by balancing a piece

of lodestone The lodestone was ground into the shape of a serving spoon thatwas placed on a bronze plate as shown in Fig 1.2 Its handle miraculouslypointed to the south

Rather than navigation, these simple direction pointers were likely used for

feng shui3or geomancy, the technique of achieving harmony with the forces ofnature by properly aligning buildings and placing of objects In particular, fengshui seeks to optimize the attractive and repulsive forces of magnetic fields thataccording to ancient Chinese philosophy surrounds all objects In the context

of magnetic energy it is interesting that much later, around 1780, Franz AntonMesmer formulated a healing method on the belief that living bodies could bemagnetized and healed – “mesmerized” – by magnetic fields [4] His influence3

Feng shui (also fung shui), which translates literally as “wind water”, is an cient Chinese philosophy and practice based on the principle that all living things

an-in the universe are subject to the control of the environment It is still widely ticed today and tries to achieve harmony with the eight elements of nature – heaven,earth, hills, wind, fire, thunder, rain, and ocean Also important are energies such

prac-as the air or “chi” and the magnetic energy, prac-as are the spirits of yin (female-pprac-assive)and yang (male-active)

was so strong that his name has passed into the English language, an honoraccorded to few.4

The development of civilization has been defined by mastering the duction and use of materials To our knowledge, magnetic direction pointers

pro-or compasses were first used fpro-or navigation in China in the late 11th pro-or early12th century and the compass became known in Europe sometime later in the12th century Without magnetic materials in the form of a compass, the greatvoyages of discovery may not have taken place and the history of the worldmight have evolved differently!

The first scholarly treatment of magnetism is attributed to the French sader and scholar Peter Peregrinus (Pierre P`elerin de Maricourt) who in 1269

cru-wrote an extended letter, an epistola, that described facts known about

load-stones and discussed how to make instruments with them [3] Three centurieslater William Gilbert (1540–1603), a medical doctor and gentleman scientist,built on this work and conducted a truly systematic study of magnetism, sum-

marized in his famous treatise De Magnete, published in 1600 He proposed

that the earth itself is a giant magnet, with a field similar to that of a barmagnet He also suggested that the magnetic poles do not coincide with thegeographic ones defined by the earth’s axis of rotation This explained earlierobservations of navigators like Columbus, who noted discrepancies betweenthe direction of a compass needle and directions indicated by the stars Theearth’s field was modeled in detail later around 1835 by Carl Friedrich Gauss(1777–1855).5

Until 1819 only one kind of magnetism was known, the one produced bylodestones or by iron compasses that had been magnetized by lodestones.6Over the following years the world of magnetism was revolutionized by thework of four people

In 1819 Hans Christian Ørsted (often spelled Oersted) (1777–1851) erved the magnetic force exerted on a magnetic needle by the electric current

obs-in a nearby wire A year later the French scientists Jean-Baptiste Biot (1774–1862) and Felix Savart (1791–1841) derived the magnetic field around a cur-rent carrying wire and during 1820–1825 Andr´e Marie Amp`ere (1775–1836)considered the forces between current carrying wires This led to the famouslaws named after the discoverers

4

Mesmer’s teachings were based on earlier claims by Paracelsus (1493–1541) that

magnets could be used for healing In addition, Mesmer claimed that animal netism was residing in humans, and that healing could proceed by exchange of a

mag-“universal fluid” between him and his patients, without the explicit use of magnets.5

The origin of the earth’s magnetic field is not well understood but is attributed

to turbulent motions within electrically conductive liquid Fe in the earth’s core (seeFig 3.2)

6

It is interesting to note that compass needles were typically made of iron whichhas a larger saturation magnetization than lodestone However, because Fe has amuch smaller coercivity than lodestone the needle often had to be remagnetized by

a lodestone that was carried on board of ships [4]

Classical electromagnetism peaked with the work of two of the greatestphysicists of the 19th century, the experimentalist Michael Faraday (1791–1867) and the theorist James Clerk Maxwell (1831–1879) [1] In 1831 Fara-day discovered electromagnetic induction, and in 1845 he discovered a directconnection between magnetism and light: the magneto-optical or Faraday ef-fect [11] The magneto-optical Faraday effect is the change of light polarization

in transmission through a magnetized material The same effect in reflection

was discovered in 1876 by the Scottish physicist John Kerr (1824–1907), and

is called the magneto-optical Kerr effect in his honor Faraday’s ideas

deve-loped in his book Experimental Researches in Electricity, and in particular,

his discoveries of electric motors, generators, and transformers, have becomethe foundation of the industrialized society We shall come back to this point

at the end of this section, in conjunction with the importance of strong manent magnets

per-Maxwell placed Faraday’s notion of a connection between electricity and

magnetism on a firm mathematical footing, developed in his book Treatise

on Electricity and Magnetism This constituted the birth of electromagnetism

and the electromagnetic field Today the concept of a “field” is a cornerstone

of physics In 1855 Wilhelm Eduard Weber (1804–1891) had derived a value

1/ √

µ0
0 = 3.1074 × 108m/s in laboratory based experiments but could notunderstand why this was close to the speed of light This connection was made

by Maxwell who through studies of the equations describing electric and

mag-netic fields was led to the value c = 1/ √

0µ0 Maxwell concluded that light is

a form of electromagnetic wave The connection between magnetism and lighthad been established Even today we still marvel at the power of Maxwell’sequations and our continued struggle to comprehend their full content makes

it even more remarkable that they were derived as early as 1864 – they areone of the truly great achievements in physics!7

Maxwell’s theories and their experimental verification by Heinrich Hertz(1857–1894) in Germany, who discovered radio waves in 1888, today are thebasis for global communications at the speed of light It is fair to say thatMaxwell’s theory became accessible mostly through Hertz and the theoreticalteachings of Henri Poincar´e (1854–1912) in France The 19th century deve-lopment of magnetism concluded with Pieter Zeeman’s (1865–1943) discovery

in 1896 of the effect named after him The century was crowned by the covery of the electron by Joseph John Thomson (1856–1940) in 1897, andindependently around the same time by Emil Wiechert (1861–1928) [13].The understanding of magnetic phenomena in the 20th century largelyconcentrated on the development of an atom-based picture [2] While corre-spondence between Augustin Jean Fresnel (1788–1827) and Amp`ere alreadymentioned the idea of microscopic currents as the origin of magnetism, a for-

dis-7Maxwell’s work was already deeply appreciated during his lifetime For example,Ludwig Boltzmann wrote full of admiration “Was it a God who wrote these symbols

.?” [12]

Fig 1.3 Postcard sent by Walther Gerlach to Niels Bohr on February 8, 1922 In

translation it says “Honorable Mr Bohr, here [is] the continuation of longer work

(see Z Phys 8, 110 (1921)) The experimental proof of directional quantization We

congratulate [you] on the confirmation of your theory! With respectful greetings,yours truly, Walther Gerlach.” From [15]

mal treatment was not developed until 1907 when Pierre Weiss (1865–1940)introduced a theory of ferromagnetism based on a molecular field concept [14].His theory, combined with that of Paul Langevin (1872–1946), explained theferromagnetic–paramagnetic transition observed by Pierre Curie (1859–1906)

at the so-called Curie temperature

In 1913 Niels Bohr (1885–1962) first postulated that the angular tum of electrons is quantized and that orbital magnetic moments are asso-ciated with orbiting electron currents An elegant experiment by Otto Stern(1888–1969) and Walther Gerlach (1889–1979) in 1921 showed the splitting

momen-of a beam momen-of Ag atoms upon traversing a nonuniform magnetic field due toquantized spin orientation The important experiment is discussed in detail

in Sect 3.5.1 A postcard sent by Walther Gerlach to Niels Bohr on ary 8, 1922, showing the refined results of the original experiment is shown inFig 1.3 The postcard shows photographs of the recorded pattern of Ag atomswithout (left) and in the presence of (right) a magnetic field It is interest-ing that the observed splitting into a doublet was incorrectly interpreted as

Febru-arising from an orbital magnetic moment with l = 1 and m = ±1, as evident

from Gerlach’s note on the postcard in Fig 1.3 He believed his experiment toconfirm Bohr’s theory of orbital angular momentum At the time, the concept

of spin was still unknown The proper explanation of the splitting is due to

the fact that Ag atoms have a single electron in their outer shell with s = 1/2, and so the splitting is actually due to the states m s=±1/2.

In order to account for the observed splitting of the emission lines ofalkali atoms in magnetic fields, called the “anomalous Zeeman effect” (see

Sect 6.6.1), Wolfgang Pauli (1900–1958) asserted in January 1925 that no twoelectrons may occupy the same states and cannot be described by the same

set of quantum numbers, the famous principle later named by Dirac the Pauli

exclusion principle It is remarkable that at the time of Pauli’s paper [16] the

electron spin had not yet been discovered Instead of today’s quantum

num-bers n, l, m l , m s, Pauli’s paper used a different, not easy to understand, set ofquantum numbers He realized that a satisfactory explanation of the anom-

alous Zeeman effect required more than the three quantum numbers n, l, m l

and called this a “Zweideutigkeit” (two-valuedness) of the quantum properties

of the electron without specifying its origin [17] The important step of tifying the “Zweideutigkeit” with the electron spin was taken by Uhlenbeckand Goudsmit later that year, in October 1925 [18–20] (see later)

iden-The three year period 1925–1928 constituted a quantum jump in physics

It saw the development of quantum mechanics by Werner Heisenberg (1901–1976) and Erwin Schr¨odinger (1887–1961) and the introduction of the electronspin The idea of a “spinning electron” was mentioned for the first time byArthur Holly Compton (1892–1962) in 1921 for reasons that were wrong andunconvincing [20] Unaware of Compton’s suggestion, George E Uhlenbeck(1900–1988) and Sam A Goudsmit (1902–1978) in 1925 used the fine structure(spin–orbit splitting) in atomic spectra to hypothesize the existence of theelectron spin [18–20] The revolutionary idea was the fact that the electronicspin had only half, ¯h/2, of the natural integer unit of angular momentum.

The spin had independently been proposed in early 1925 by Ralph de LaerKronig (1904–1995) [2] who told Pauli about it Pauli objected to Kronig’ssuggestion of a half integer spin because it led to a discrepancy of a factor of

2 in the calculation of the fine structure splitting Kronig did not publish hisidea owing to Pauli’s objection, as evidenced by the letter in Fig 1.4

In contrast, when Uhlenbeck and Goudsmit showed their idea to theirmentor Paul Ehrenfest (1880–1933), he encouraged them to proceed withpublication For Uhlenbeck and Goudsmit, ignorance was bliss since they wereunaware of the factor-of-2 problem They worried more about the fact that itdid not make sense to associate the spin with a classically rotating chargedelectron The factor of 2 pointed out by Pauli was explained by a celebratedcalculation of Llewellyn Hilleth Thomas (1903–1992) [20, 21] who in 1926showed it to be due to a reference frame effect Uhlenbeck and Goudsmithad been right after all!8

The concept of the spin with half-integer angular momentum is indeedquite amazing and even today its origin is not easily understandable It nat-urally fell out of the celebrated relativistic theory of Paul Dirac (1902–1984),who in 1928 treated an electron in an external electromagnetic field, with-

8

Much has been written about the discovery of the spin and the fact that beck and Goudsmit (or Kronig) did not receive the Nobel Prize For a more detailedaccount and more references the reader is referred to the Pauli biography by Charles

Uhlen-P Enz [22], especially Chap 5

Fig 1.4 Part of a letter sent by Thomas to Goudsmit on March 26, 1926 [20].

It chronicles some of the events associated with the discovery of the spin It reads

as follows “I think you and Uhlenbeck have been very lucky to get your spinningelectron published and talked about before Pauli heard of it It appears that morethan a year ago Kronig believed in the spinning electron and worked out something;the first person he showed it to was Pauli Pauli ridiculed the whole thing so muchthat the first person became also the last and no one else heard anything of it Whichall goes to show that the infallibility of the Deity does not extend to his self-styledvicar on earth.”

out explicitly introducing the electron spin [23, 24] Dirac’s quantum dynamics (QED) theory correctly described the magnetic properties of theelectron and its antiparticle, the positron, but it proved difficult to calcu-late specific physical quantities such as the mass and charge of the particles.This was overcome in the late 1940s when Sin-Itiro Tomonaga (1906–1979),Julian Schwinger (1918–1994), and Richard P Feynman (1918–1988) inde-pendently refined and fully developed QED9 An important feature of QED

electro-is that charged particles interact by emitting and absorbing photons, so thatphotons are the carriers of the electromagnetic force

9

The theories by Tomonaga, Schwinger, and Feynman were later shown to beequivalent by Freeman J Dyson (b 1923)

In 1928, the year of Dirac’s QED theory, there was another importantbreakthrough in the history of magnetism with Heisenberg’s formulation of aspin-dependent model for the exchange interaction [25] The molecular fieldpostulated by Weiss could now be interpreted as having its origin in the ex-change interaction The introduction of the strong, short-range exchange inter-action constituted the birth of modern magnetism theory, which has its roots

in, both, quantum theory and relativity In a series of papers starting in 1932,Louis N´eel (1904–2000) developed the concept of antiferromagnetism [26].N´eel’s ideas of antiferromagnetic and ferrimagnetic spin alignments were laterverified by neutron diffraction, pioneered by Clifford G Shull (1915–2001) Inthe mid 1930s, band theory was first applied to magnetic systems by Neville

F Mott (1905–1996) [27], John C Slater (1900–1976) [28, 29] and Edmund

C Stoner (1899–1968) [30, 31] Today further developments of this theoryare a cornerstone of modern magnetism, explaining the noninteger values ofmagnetic moments

While research in magnetism today is largely driven by the fast movingpace of information technology, especially data storage and memory applica-tions, one cannot forget that from a world-wide economic and societal point ofview another more mundane application of magnetic materials may be more

important It is the use of high energy product permanent magnets that

under-lie the generation and use of electricity Under the term “high energy productmagnets” one understands magnets which exhibit a magnetization loop that isboth wide (maximum coercive field) and high (maximum magnetization) [32].Such magnets facilitate the reduction of the size and the weight of a devicemade from them, for example, electric motors and audio speakers The his-torical increase of the energy product, formally defined as the product of the

applied field and the magnetic induction (H B)max, is illustrated in Fig 1.5.Today the strongest commercial magnet is Nd2Fe14B, developed in 1984

by Croat et al [34] and Sagawa et al [35] Permanent magnets are key ponents of electrical generators.10On a global scale, it is well established thatthe economic output of nations today is strongly correlated with their use

com-of electricity since electrification makes an economy more efficient [36] Forexample, today about half of the US energy is consumed as electricity andthe US electricity retail sales amount to about 250 billion dollars per year, orabout 2.5% of the US gross domestic product (GDP) It is therefore important

to keep in mind the future development of improved permanent magnets Suchwork was given new impetus by the suggestion of spring magnets by Knellerand Hawig in 1991 [37] and Stromski and Coey in 1993 [38] Recent research

on spring magnets has been reviewed by Bader [39] More information on theproperties of magnetic materials can be found in O’Handley’s book [40]

10They have also revolutionized accelerator technology, allowing the construction

of permanent magnet wigglers and undulators at third generation synchrotron diation sources

Hard ferrites

Samarium–cobalt Neodymium–iron–boron 1,000

Fig 1.5 Historical evolution of the performance of permanent magnets, defined by

their energy product (H B)max Shown are five principal industrial magnet families.Note that the ordinate has a logarithmic scale Figure taken from [33] after [32]

The most advanced applications of magnetism today are closely related tothe technology underlying magnetic storage and memory [41, 42] As early as

1888 magnetic recording was proposed by Oberlin Smith and the first ful magnetic recording device, the telegraphone, was patented by ValdemarPoulsen in 1894 [41, 43] In 1949, physicist An Wang at Harvard created a de-vice based on small ferrite rings, so-called “cores”, that could be switched bycurrent flow through wires that penetrated the rings, as illustrated in Fig 1.6

success-In the 1950s this led to the development of nonvolatile magnetic core

memo-ries which became the dominant computer memomemo-ries in the early 1960s but

were replaced by semiconductor memories in the 1970s.11

For the last 40 years magnetism has been used to store information incomputers This 50 billion dollars per year industry is based and dependent

on fast developing concepts It has fuelled a renaissance in magnetism researchbased on artificially engineered thin film structures [44, 45] Nonvolatile mag-netic memory is also making a comeback as so-called MRAM for magneticrandom access memory [46] From a science point of view the last 15 yearshave been particularly exciting and these developments and envisioned futureconcepts and technologies will be extensively discussed in this book

11Wang’s patent was not granted until 1955, and by this time core memory wasalready in use This started a long series of lawsuits, which eventually ended whenIBM paid Wang several million dollars to buy the patent outright

~500 µm Magnetic core memory (1950s)

Fig 1.6 Schematic of magnetic core memory used in computers in the 1960s.

Currents through two wires were used for writing “bits”, i.e., opposite magnetizationstates shown as white and black arrows, in small ferrite ceramic rings The thirdwire was used for reading changes in magnetization through induction

1.3 Magnetism, Neutrons, Polarized Electrons,

and X-rays

Early experiments to elucidate magnetic phenomena and materials were based

on the measurement of forces and torques exerted on “samples” placed intomagnetic fields produced by current flow through wires Later experimentsinvolved measurements of the magneto-optical Faraday (transmission) andKerr (reflection) effects Today the Kerr effect forms the basis of the magneto-optical recording technology by utilizing powerful yet small semiconductorlasers The laser was proposed by Arthur L Schawlow and Charles H Townes

in 1958 [47] and the first laser, made out of synthetic ruby, was built byTheodore H Maiman in 1960 It is a powerful research tool for the study ofmodern magnetic materials, typically in the form of thin films, and scanningand imaging Kerr microscopy gives microscopic information with a resolutionnear the diffraction limit of light (about 200 nm) This diffraction limit is one

of the Achilles’ heals of visible light (and lasers) for the study of matter Theother one is the strong absorption of visible light by matter, making it difficult

to look into or through many bulk materials In principle, these limitationswere overcome by Wilhelm Conrad R¨ontgen’s (1845–1923) discovery of X-rays

in 1895 [48] but the use of X-ray for the study of magnetic materials had towait for nearly another century, as discussed later

With the development of neutron diffraction and spectroscopy techniques

in the 1940s and 1950s it was finally possible to determine the spin structure on

an atomic level The seminal contribution of neutron techniques to magnetism

is reflected by the October 1994 press release by the Royal Swedish Academy

of Sciences on the 1994 Nobel Prize in Physics, won by Bertram N Brockhouse(1918–2003) and Clifford G Shull (1915–2001), “Neutrons are small magnets,

as are the atoms of a magnetic material When a neutron beam strikes suchmaterial, the neutrons can therefore change direction through magnetic inter-action with the atoms of the material This gives rise to a new type of neutrondiffraction which can be used to study the relative orientations of the small

atomic magnets Here, too, the X-ray method has been powerless and in this

field of application neutron diffraction has since assumed an entirely dominant position It is hard to imagine modern research into magnetism without this

aid.”

At the time of this press release efforts were already underway to changethe role of X-rays in magnetism This relatively recent and important deve-lopment will be discussed later The last 30 years have seen another importantdevelopment, the generation and manipulation of spin polarized electrons [45].This development has culminated in phenomena like giant magnetoresistanceand “spintronics” We shall see later that studies by means of polarized elec-trons and X-rays have provided important new information Today one couldrephrase the last sentence of the above quote by the Nobel Prize Commit-

tee: It is hard to imagine modern research into magnetism without polarized

electron and X-ray probes.

Within this book we shall not discuss the technique and applications ofneutron scattering for the study of magnetic materials This has been doneextensively by others such as Bacon [49], Squires [50], Balcar and Lovesey [51],

or more recently by Fitzsimmons et al [52] and in the book on magnetismtechniques by Zhu [53] Another reason is that in today’s magnetism research,materials with nanoscale dimensions and phenomena associated with surfaces,thin films, and interfaces are of prime importance This has led to an increaseddemand for techniques with high sensitivity to small amounts of magnetic

material or a small number of magnetic atoms The atomic sensitivity of

different techniques based on neutrons, electrons or X-rays may be expressed

by a figure of merit per atom per second (FOM), defined by the product of

the respective atomic interaction cross-section, the available incident flux, andthe square of the magnetic contrast, as done in Table 1.3

In the Table we have assumed that we can use samples as large as

10 mm× 10 mm so that we list the incident flux per cm2 For smaller ples the neutron flux and FOM would be reduced proportional to the areawhile the electron and photon flux remains unchanged down to sample areas

sam-of mm2 or less The Table shows that the use of neutrons with a small FOM

is unfavorable for nanoscale magnetism research where the quest is for toolsthat can image small magnetic structures in short observation times Neu-tron techniques have been and remain important for studies of bulk materialswhere the small FOM per atom is overcome by the large number of contribut-ing atoms In contrast, electron, resonant X-ray, and optical techniques offer a

Table 1.1 Comparison of factors determining the interactions of neutrons, low

en-ergy (< 10 eV) electrons, X-rays, and optical photons with magnetic materials such

as the ferromagnets Fe, Co, and Ni For neutrons and X-rays, the listed elastic

scat-tering cross-sections σ refer to the magnetic cross sections per atom, for all other

cases we list the combined charge and magnetic cross sections and indicate the

mag-netic contribution through a fractional value for the magmag-netic contrast P We also list the incident monochromatic flux per appropriate experimental bandwidth Φ, and the relative figure of merit per atom per second, defined as σΦP2 The true magneticsignal for a given sample will depend on the probed number of magnetic atoms inthe beam For a given lateral sample size the number of atoms can be increased bymaking the sample thicker but the maximum number of probed atoms is inverselyproportional to the cross-section Therefore neutron techniques can overcome thelimited scattering signal per atom by use of large and thick samples

technique atomic cross- magnetic incident figure of merit

section σ contrast P flux Φb 10−7 σΦP2[barn/atom]a [s−1cm−2BW−1]

1electrons El Scatt 1× 108

0.5 1× 1010

2.5 × 1010

Res El Scatt.d 5× 103 0.5 1× 1012 1.25 × 108Res Abs.d 5× 106

0.3 1× 1012

4.5 × 1010light Kerr Effect 5× 106

0.01 1× 1016

5× 1011 a

Total resonant cross-section at 3d transition metal L-edge

large sensitivity per atom and are well suited for the studies of surfaces, thinfilms and nanostructures

Of the various techniques the magneto-optical Kerr effect (MOKE) has avery high FOM and the technique is relatively simple in practice [54,55] Con-sequently, it is the technique that enjoys the greatest popularity, particularlyfor the study of ultrafast magnetization dynamics where the availability ofshort and intense laser pulses is a great asset [56, 57] The main drawback ofthe Kerr technique is its limited spatial resolution which arises from the rela-tively long wavelength of near-visible light This makes MOKE unsuited forimaging the magnetic structure of nanoscale magnetic elements It is thereforeexpected that in the future the use of X-ray techniques will increase, especiallyfor the study of nanoscale dynamics as discussed in Chap 15

In the following we shall discuss the developments of electron and X-raytechniques

1.3.1 Spin Polarized Electrons and Magnetism

Quantum theory as well as the discovery of electron-spin resonance in 1945

by Evgeny Konstantinovich Zavoisky (b 1907) [58] had made it clear that themagnetization in Fe, Co, and Ni must be predominantly generated by the spinpolarization of the metallic electrons However, for a long time it appearedimpossible to extract spin polarized electrons from metals into vacuum byfield emission or photoemission techniques despite expectations that the spinshould be conserved in these emission processes The problems were not due

to the lack of a method to detect the spin polarization since “Mott detectors”were already used by H Frauenfelder [59] in 1957 to detect the spin polari-

zation of the electrons emitted in β-decay, verifying parity violation in weak

interactions as suggested by Lee and Yang in 1956 [60] Mott scattering isbased on the spin–orbit coupling in the Coulomb scattering of electrons fromheavy nuclei such as Au, discussed in Sect 3.5.2 In the end, the inability

to extract spin polarized electrons from ferromagnetic cathodes proved to bemainly due to improper surface preparation

In 1969 Siegmann and collaborators [61, 62] showed that once atomicallyclean surfaces of the magnetic metals are prepared, photoelectrons emittedfrom all kinds of ferromagnets exhibit sizeable spin polarization Figure 1.7shows a congratulatory postcard sent to H C Siegmann by Walther Gerlach

in March 1969 Over the last thirty-plus years Spin-polarized photo-emissionspectroscopy (SPES) has been developed into a powerful tool for the deter-mination of the occupied spin polarized band structure of magnetic solids,particularly near or at the surface The surface sensitivity arises from thevery short mean free path of electrons in metals, which is of order 1 nm.SPES provides a rigorous test of our understanding of magnetism and theconnection between electron emission and the electronic structure

Spin polarized electron spectroscopies in their various forms were tial in the development of surface and thin film magnetism, an area that hasprovided the basis for a renaissance in magnetism research and enabled thedevelopment of innovative magnetic technologies over the last 15 years Thenew structures of interest have nanoscale sizes in at least one direction so thatinterfacial and surface properties often dominate their static magnetic struc-ture and transport behavior (see Chap 13) The power of SPES techniqueslies in their sensitivity to the spin polarized band structure of magnetic solids,

essen-be it in the form of insulators, metals, or the exotic half-metallic ferromagnets,

distinguished by their complete spin polarization at the Fermi-level EF

As an example of the insight that can be obtained by measurement of thespin polarization of photoelectrons, we show in Fig 1.8 results for the oldestmagnetic material, magnetite Fe3O4, obtained in 1975 by Alvarado et al [63]with natural crystals found in a dry river bed close to Zermatt, Switzerland.For a long time, the electronic structure of the ferrites was a subject of specu-lation [64] due to the ambiguities of spectroscopies without spin analysis The

Fe O -spectra are complex due to the coexistence of 3 different Fe-ions and the

Fig 1.7 Postcard sent by Walther Gerlach to H C Siegmann on March 28, 1969.

In translation it says “My dear Siegmann, Thank you very much and congratulations

on the nice work It pleases me very much I wish you much success in the future –first of all happy holidays for your wife and you Always, yours Walther Gerlach.Please also extend my greetings to Mr Busch Munich, 28 3 69”

oxygen 2p-bands The ambiguities in the interpretation are overcome by spin

analysis The negative spin polarization at photoelectric threshold shows thatthe highest lying levels are occupied with minority spins This confirms thefamous model for the metal/insulator or Verwey-transition at 119 K in Fe3O4

put forward by Mott [64] that the electrical conduction at EFis generated byhopping of minority spins The data shown in Fig 1.8 also provide evidence

that magnetite is a half-metallic oxide, i.e., that conduction occurs in one

spin channel only We shall discuss the electronic structure and magnetism ofmagnetite in more detail in Sect 7.7.4

While conventional magnetism techniques typically measure the magneticsignal of the bulk of a ferromagnet or the combined signal from different layers

in sandwich-like structure, SPES can probe the surface magnetism

4

−40

−20 0 20 40 60

F

Fig 1.8 Spin polarization of photoelectrons as a function of photon energy from

single crystal magnetite, Fe3O4, measured by Alvarado et al in 1975 [63] The energy

dependence of the spin polarization P supports the half-metallic character The high value of P suggests that the energy of the oxygen 2p-bands lies below that of the Fe 3d-levels (see Sect 7.7.4)

dent of the magnetic properties of the underlying material because of its smallprobing depth Photoemission spectra from the elemental ferromagnetic met-

als Fe, Co, and Ni are complex because the 3d-states are not separated from the 4s, p-states as in magnetite Additionally, a rich mixture of surface reso-

nances and surface states is superimposed onto the bulk states [65] Initially, itwas difficult to understand the observations of SPES even in the simplest case

of threshold photoelectrons The difficulties in the interpretation arose becausethreshold photoemission was in fact the first manifestation of the unexpec-tedly strong preferential scattering of minority spins in ferromagnetic metals,today often called the “spin filter effect” [66], as discussed in Sect 12.6.1.The low energy secondary electrons emerging from the ferromagnetic met-als exhibit as much as a threefold enhancement of the degree of spin polariza-tion over that expected from the magnetic moment This again is due to thespin dependence of the electron scattering generating the low energy electroncascade The high polarization of the low energy cascade is used in scanningelectron microscopy with polarization analysis (SEMPA), pioneered by Koikeand Hayakawa in 1984 [67] and developed in the following years mostly byUnguris, Pierce, and Celotta [68], to produce stunning high resolution im-ages of magnetic structures at surfaces with a spatial resolution of ∼10 nm.

Figure 1.9 shows a particularly beautiful SEMPA image which pictures the

Fe whisker [001]

Cr wedge 46 layers

Fe film

Fig 1.9 Magnetic image, recorded by scanning electron microscopy with

polariza-tion analysis (SEMPA), of a thin Fe film, separated by a wedge-shaped Cr spacerlayer from a single crystal Fe whisker [69] The indirect magnetic coupling between Feoscillates as a function of the Cr-spacer layer thickness from ferromagnetic (aligned

Fe magnetizations) to antiferromagnetic (opposed Fe magnetizations) The actualdata are shown superimposed on a schematic of the wedge structure Black and whitecontrasts in the image correspond to opposite in-plane magnetization directions

oscillatory magnetization pattern in a thin Fe film that is coupled via a Crwedge to a single domain Fe substrate [69]

In contrast to photoemission, field emission of electrons from the metalsinto vacuum yields mostly weakly polarized electrons The initial results withfield emitted electrons were nonreproducible due to improper measurement ofthe small spin polarizations in the presence of a magnetic field at the field-emission cathode However, Meservey and Tedrow discovered in 1971 thathigh spin polarization similar to the one observed in photoemission or sec-ondary emission occurs also in tunneling of electrons from the ferromagneticmetals into super-conducting Al [70] The interpretation of the sign and mag-nitude of the spin polarization observed in tunneling constituted a problem asdocumented by the letter shown in Fig 1.10, and it is still a challenge today.Spin polarized magnetic tunneling spectroscopy holds many promises for thefuture

Spin polarized photoelectrons may also be extracted from nonmagneticmaterials if circularly polarized light is used for the excitation of the photo-electrons and if spin–orbit coupling is large Such nonmagnetic photocathodesare more convenient than ferromagnetic ones since no magnetic field is present

at the cathode that can disturb the electron-optics The spin can simply beswitched from up to down by switching from right- to left-circularly polarizedlight in the excitation of the electrons For this reason GaAs-type photo-cathodes, first proposed and demonstrated in 1974 by Garwin, Pierce, andSiegmann [72, 73] are now the most common sources of polarized electrons,delivering intense, highly monochromatic, and almost completely polarizedelectron beams in which the spin direction can be chosen at will without af-fecting other beam characteristics The possibility to flip the spin separates thescattering due to the spin from the dominant scattering due to the Coulomb

Fig 1.10 Letter by Sir Neville Mott about spin polarized electron experiments

on Ni by means of photoemission [62] and tunneling [70] It indicates the problemsassociated with the interpretation of the sign of the spin polarization observed inthese experiments Mott refers to Phil Anderson’s paper [71]

interaction Over the years, spin modulated electron beams have been sively used to probe magnetism In fact, spin modulated electrons have beencalled “surface neutrons” because they are as important in surface magnetism

exten-as neutrons are in bulk magnetism

A number of striking experiments can be done with the GaAs source Ininverse photo-emission spectroscopy (IPES), the Bremsstrahlung is measuredwhen incident electrons with spin parallel or antiparallel to the magnetizationrecombine with the solid It is thus possible to measure the spin polarizedunoccupied band structure and to detect magnetism in the various surfacestates When an electron beam with spin at an angle to the magnetizationtraverses a magnetic solid or when it is reflected from a magnetic surface, thespin of the electron precesses at a very fast rate due to the exchange inter-action It also rotates into the direction of the magnetization due to inelasticscattering Both, precession and rotation can be separately measured byobserving the position of the spin polarization vector after the interaction.This directly determines the exchange interaction as it depends on electronmomentum and energy as well as the inelastic scattering events that are es-

e

Fig 1.11 Strained GaAs/GaAsP superlattice cathode developed at the Stanford

Linear Accelerator Center (SLAC) for the creation of spin polarized relativisticelectron beams The structure of the cathode is shown on the left and the polarizationand quantum efficiency (QE) as a function of laser excitation energy are shown onthe right The cathode is taken from a 2-inch diameter substrate wafer onto whichlayers are grown by gas-phase molecular beam epitaxy The lattice of these layers isdistorted from cubic symmetry which increases the electron polarization created byincident circularly polarized light To avoid depolarization, the cathode is Be-dopedwith a low concentration, except in the top 5 nm the concentration is increased to

5× 1019cm−3 to improve the QE [77]

sential in many magnetic phenomena In yet another application of the GaAssource, called spin polarized low energy electron diffraction (SPLEED), themagnetic structure can be observed superimposed on the crystallographic one

In spin polarized low energy electron microscopy (SPLEEM), very low energyspin polarized electrons are reflected from the magnetic surface yielding dy-namic information on magnetic processes at surfaces at video frequencies and

at∼10 nm spatial resolution [74].

GaAs sources are also used to create polarized relativistic electron beamsfor high energy physics experiments For example, an early version of thesource shown in Fig 1.11 was used in a famous experiment in 1978 at theStanford Linear Accelerator Center (SLAC) which revealed a very small butconsequential spin dependence of 10−5 in the scattering of electrons withenergies around 20 GeV on deuterium and hydrogen [75,76] The electron spinwas oriented parallel to the beam direction to separate the electromagneticfrom the weak interaction The experiment constituted an important steptoward the confirmation of the Weinberg–Salam gauge theory of the weakand electromagnetic interactions, underlying the “Standard-Model” in whichthe two interactions are unified

Today the concepts underlying the production of spin polarized electrons

by laser excitation of GaAs are used in semiconductor based spintronics

re-search In this case the electrons are excited with circularly polarized lightfrom the valence to the conduction band with an energy that is insufficientfor photoemission from the sample The excited conduction band electrons arespin-polarized and may be manipulated or probed by a well defined secondlaser pulse [78].

In 1988, Albert Fert and collaborators in Paris [79] and Peter Gr¨unberg andcollaborators in J¨ulich [80, 81] independently12 discovered that spin selectivescattering is observed in multilayered magnetic structures as well, generatingthe phenomenon of giant magneto-resistance (GMR) In 1990 Stuart Parkin

et al [82, 83] demonstrated that GMR is present not only in single crystalmaterials but also in sputtered multilayers that are compatible with manu-facturing techniques and that through thickness control of the nonmagneticspacer layer the coupling may be changed from ferromagnetic to antiferromag-netic These discoveries have transformed magnetism, and GMR has become

an important component of high speed, high-density magnetic recording.More recently, John Slonczewski [84] and Luc Berger [85] proposed thatspin polarized electron currents can transport angular momentum from oneferromagnet to another and excite spin waves or even switch the magnetiza-tion As discussed in Sect 14.2, this idea has been verified in experiments andattracted much attention It combines interesting scientific questions related

to the dynamics of the exchange coupled spins with the promise of applications

in high density magnetic recording and storage All-solid-state spin polarizedelectron physics and spin electronics, so called “spintronics”, have become animportant topic in magnetism

Yet another basic capability of magnetometry with spin polarized

elec-tron spectroscopy includes time resolution As will be discussed in detail in

Chap 15, photoemission of electrons is a very fast process that occurs on atime scale of less than 10−15 s for kinetic energies larger than a few eV Ifcombined with pulsed lasers or photon pulses from synchrotron sources, it can

be used to generate a short pulse of photoelectrons The spin polarization ofthe photoelectron pulse can be measured It is proportional to the magne-tization of the initial electron states from which the electrons were emitted.These initial electron states can be selected by choosing the photon energy or

by selecting the energy of the photoelectrons In this way, the time scale andthe mode on which the magnetization reestablishes itself after an excitation,e.g., by the generation of electron–hole pairs, can be studied [86] The spindependence of the lifetime of electrons that have been excited to states abovethe Fermi-energy has been observed, as well [87], providing direct evidence forthe preferred scattering of minority spins in the time domain

12Note that in contrast to the publication dates, the Gr¨unberg paper was mitted to Physical Review on May 31, 1988 while the Fert paper was submitted toPhysical Review Letters on August 24, 1988

sub-1.3.2 Polarized X-rays and Magnetism

Despite the power of optical techniques for magnetic studies, we have alreadymentioned limitations set by the wavelength and energy of light Today’s mostpowerful applications of X-rays in magnetism utilize fully polarized, tuneablesynchrotron radiation, where the X-ray energy is tuned to the absorption edge

of a magnetic atom [88] This was first suggested by Erskine and Stern [89]

in 1975 by considering an extension of the magneto-optical Faraday and Kerreffects into the ultraviolet/soft X-ray region The principles underlying opticaland X-ray effects are illustrated and compared in Fig 1.12 Optical methodsrely on spin dependent transitions between valence band states at certain

wave-vector (k) points in the Brillouin zone In contrast, X-ray techniques

utilize core to valence transitions The resonant X-ray signal is element andeven chemical state specific since core level binding energies depend on theatomic number and chemical state In addition, the measured resonant X-rayintensity is quantitatively linked by sum rules with the spin and orbital mag-netic moments since it measures wave-vector integrated properties of the va-lence shell, in contrast to optical methods which measure specific wave-vectordependent transitions Finally, as dimensions enter the nanoscale, typicallyidentified with dimensions below 100 nm, visible light becomes “blind” andone needs shorter wavelength X-rays to see the magnetic nanoworld

Following the pioneering use of X-rays for magnetic studies by de Bergevinand Brunel [90] in 1972, important new developments occurred in the mid

band

Conductionband

Fig 1.12 Comparison of the processes underlying the Faraday and Kerr effects

in the visible spectral range and the processes in X-ray magnetic circular dichroism(XMCD) In the visible one typically uses linearly polarized light and measures thepolarization rotation and ellipticity of the transmitted or reflected light In XMCDone measures the difference of the absorption spectra obtained with left and rightcircularly polarized X-rays

1980s In 1985, Blume first pointed out the advantage of performing magnetic

scattering experiments by tuning to an absorption edge, so-called resonant

magnetic scattering, and developed its theory The effect was first observed in

the same year by Namikawa et al using tuneable synchrotron radiation [91].Later work by Gibbs et al in 1988 [92] clearly showed the advantage of usingthe large cross-section enhancements associated with absorption edges andthis work established X-rays as a viable alternative to neutrons for the study

of magnetic structure

In the same time period, two other developments took place which werebased on X-ray absorption spectroscopy instead of X-ray scattering In 1985,Thole, van der Laan, and Sawatzky [93] predicted the occurrence of a linearX-ray magnetic dichroism effect in near-edge X-ray absorption spectra whichwas observed by van der Laan et al in 1986 [94] Another breakthrough came

in 1987 when Sch¨utz et al [95] demonstrated a circular magnetic dichroismeffects in X-ray absorption By the late 1980s the stage was set for exploringand refining X-ray techniques for magnetic studies

In the 1990s it became clear that soft X-rays play a particular importantrole for magnetic studies [98,99] The power of soft X-rays arises from the factthat the most important absorption edges for resonant magnetic studies, the

L-edges (2p core shell) of Fe, Co, and Ni and the M-edges (3d core shell) of the

rare earths fall into the 700–1,500 eV range These absorption edges exhibit

large magnetic effects and through dipole allowed 2p → 3d and 3d → 4f

transitions provide access to the magnetic properties of the important 3d and 4f valence electrons which dominate the magnetic properties of transition

metals and rare earths, respectively Figure 1.13 illustrates the relative size ofthe magnetic dichroism effect, defined as the difference in absorption betweenright and left circularly polarized X-rays, near the Co K-edge and the L-edges.The effect is seen to be larger at the soft X-ray L-edge by a remarkable factor

of 2,000

The experimental soft X-ray studies triggered theoretical work on the formation content of the experimental spectra, leading to fundamental sumrules linking the measured dichroic intensities to spin and orbital magneticmoments and their anisotropy [100–102] The importance of the sum rules lies

in-in the fact that they allow the use of X-rays for quantitative magnetometry.The final important developments were the demonstrations that X-rays can beused for domain imaging in ferromagnets in 1993 [103]13and antiferromagnets

in 1999 [105–107]14 With the beginning of the new millennium versatile perimental soft X-ray tools were in place to tackle problems in the field ofmagnetism

ex-13

An independent yet later paper in 1993 published by Schneider et al [104] alsodemonstrated magnetic imaging with X-rays It used Auger electron detection, incontrast to total or secondary electron yield detection employed by St¨ohr et al [103]

14Following first attempts by Spanke et al in 1998 [108] the first clear images ofantiferromagnetic structure were obtained by St¨ohr et al in a series of experimentsstarting in 1999 [105–107]

−1.0

−0.500.5

+ -0.8

Fig 1.13 The top row shows absorption spectra near the L-edge (left ) [96] and

K-edge (right ) [97] of magnetized Co metal with magnetization and photon

angu-lar momentum parallel and antiparallel, respectively For the Co K-edge the twospectra are indistinguishable on the plotted scale In both cases the spectra havebeen normalized to the same average edge jump, which was set to 1 Underneathare shown the XMCD specta, defined as the difference spectra of the polarizationdependent absorption spectra Comparison of the size of the XMCD effect revealsthat the L-edge XMCD effect is larger by a factor of 2,000

An illustrative example of the development of X-ray science in the first 100years is shown in Fig 1.14 The figure compares one of the first X-ray imagesrecorded by R¨ontgen with the first magnetic image recorded by St¨ohr et al.with soft X-rays in 1993 [103] The figure illustrates several important generalpoints X-rays can be used for electron density as well as for magnetic imaging.While high energy X-rays are most suitable for imaging of bulk objects, softX-rays are particularly well suited for imaging the structure of thin films, e.g.,magnetic domains Kortright et al [44] have discussed the opportunities inthe study of magnetic materials and phenomena by means of X-rays